Similar to the Performance Ratio, the ratio of the power (DC or AC) to the DC STC power rating compared to the irradiance divided by the reference irradiance gives the normalized efficiency, $$\eta_N$$ [1]:
$$\eta {_{N}}=\frac{P/P_{STC}}{E_{POA}/E_{ref}}$$
where P is the measured power, $$P_{STC}$$ is the STC rated power, $$E_{POA}$$ is the plane of array irradiance, and $$E_{ref}$$ is the reference irradiance (1,000 W/m^2)
One of the shortcomings of both the performance ratio (PR) and the normalized efficiency is that they are sensitive to temperature variations, as the change in temperature leads to a change in efficiency and power, and subsequently energy. For the PR, when plotted over a full year, it typically exhibits lower values in the warm parts of the year and higher values in the colder times of the year.
The change in efficiency or power of a photovoltaic module (or array) can be quantified using the temperature coefficient of power ($$\gamma$$), which allows the power (or efficiency) of a module to be modeled for a certain temperature. For crystalline silicon technologies, $$\gamma$$ is in the range of -0.3%/deg C (newer technologies) to -0.5%/deg C (older technologies).
Power at a given cell temperature, $$T_{cell}$$ is calculated as:
$$P(T)=P{_{STC}}\left ( 1+\gamma \left ( T{_{cell}-T_{STC}} \right ) \right )=P_{STC}\left ( 1+\gamma \Delta T_{STC} \right )$$,
where $$T_{STC}$$= 25 deg C.
The temperature-corrected form of power ($$P^{*}$$) can be expressed as:
$$P^{*}=\frac{P(T)}{1+\gamma \Delta T_{STC}}$$.
By using the temperature-corrected form of the power, the temperature-corrected normalized efficiency, $$\eta _{N}^{*}$$
$$\eta _{N}^{*}=\frac{P^{*}/P_{STC}}{E_{POA}/E_{STC}}$$
The temperature-corrected values should then indicate the performance of the module or system, as if it continuously works at the STC temperature. Deviations in the performance can then be more easily attributed to other effects, for example the irradiance spectrum or inverter efficiency at lower irradiances.
The normalized efficiency can be calculated using both reference cell and pyranometers data. For rapid irradiance changes, a reference cell will deliver better results. For energy comparisons using the performance ratio, pyranometers are often recommended [2], although reference cells may also be used.
The recommended instruments for irradiance (reference cell) or irradiation (pyranometers) are indicated in the figure, although as shown, they may be applied for the other metric as well. In such cases, care must be taken for the interpretation of results: as a reference cell has a technology-specific spectral response, it will generally indicate a lower irradiance and irradiation value than a pyranometer. The PR calculated using reference cell data will then be higher than using pyranometer data.
References:
[1] Herteleer, B., B. Huyck, F. Catthoor, J. Driesen and J. Cappelle (2017). “Normalised efficiency of photovoltaic systems: Going beyond the performance ratio.” Solar Energy 157(Supplement C): 408-418.
[2] “Analytical Monitoring of Grid-connected Photovoltaic Systems: Good Practices for Monitoring and Performance Analysis” – Achim Woyte and Mauricio Richter and David Moser and Nils Reich and Mike Green and Stefan Mau and Hans Georg Beyer, Report IEA-PVPS T13-03:2014
Page content contributed by Bert Herteleer, KU Leuven, ESAT-ELECTA